In how many ways can a class of 32 students select a president, vice president, treasurer, and secretary?

How many different selections of three books can be made from a set of fifteen books?

n how many different ways can we select a committee of a president, vice president , and a secretary from 15 applicants?

In how many ways can five people be divided into two groups of one person and one group of three people?

A city soccer league has 8 teams.  In how many ways could the league assign first, second, and third-place trophies at the end of the season?

Three rooms in a university residence contain three beds, two beds, and five beds, respectively. In how many ways can ten students be assigned to these rooms?

In how many ways can a committee of 12 men and 12 women be selected from a panel of 36 men and 40 women?

Faculty at a certain university need to create a committee to evaluate the general studies curriculum offered on campus. If there are 30 faculty members and they must select a chair, vice chair, secretary and 6 additional faculty members to be on the committee, in how many ways can the committee be formed?Number of possible groups =

How many ways can a treasurer, vice president, and president be chosen from a group of 15 candidates?

In how many ways can a committee of three men and four women be formed from a group of eleven men and ten ​women?